There may be a couple of reason people feel DRW are more stable. Emotional response of the driver that thinks its more stable or in Fords case a rear sway bar is standard on a dually and optional on a SRW. I seriously doubt one can tell the difference in a new F350 SRW and F350 DRW if they both have sway bars and the truck is with in tow specifics. The notion that it has more tires makes it stable is questionable if one considers that the truck spring interfaces are equivalent between SRW and DRW. The frame pivots the same on the hangers and overload springs not the tires.
Remember fifth wheel trails by nature pull in a stable manner.....